How to determine the adsorption energy of the surfactant’s hydrophilic head? How to estimate easily the surface activity of every simple surfactant?

Abstract

A definite way to determine the adsorption energy of the surfactant’s hydrophilic head on the air water interface is presented. For this purpose, the Davies adsorption theory and the most advanced version of Helfand–Frish–Lebowitz adsorption theory were applied to the surface tension isotherms of homologous series of sodium alkyl sulfate (CnH2n+1SO4Na, n=7–12), thus deriving the equilibrium adsorption constant, the cross-sectional area of the surfactant molecule, the interaction coefficient and the cohesion constant versus the number of the carbon atoms into the alkyl sulfate molecule. Thus, the total adsorption energy of each particular homolog was calculated in line with the latest development of the adsorption theory, thus calculating the dimensionless adsorption energy of the hydrophilic head Ehead/kBT. In our particular case (SO4−) we calculated Ehead/kBT=−2.79, which indicates the strong propensity of the SO4− to be surrounded by water molecules. The procedure for calculation Ehead/kBT does not depend on the charge of the hydrophilic head. Similarly, we calculated Ehead/kBT of another six well known in the literature hydrophilic heads (COOH, OH, DMPO, DEPO, N(CH3)3+, and NH3+), indicating that the adsorption energy of the CH2 group depends slightly on the type of the hydrophilic head, but it affects substantially the adsorption energy of the whole surfactant molecule. Finally, we defined and validated a parameter called adsorption capacity of surfactants with simple molecular structure, for easy estimation of their surface activity. Linear dependence between the CMC of ionic surfactants and their adsorption capacity was established.